To test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly assigned to the 3 treatments. You are given the results below. TreatmentObservationA20302533B22262028C40302822 Note: rearrange this to (columns) in excel: A B C20 22 4030 26 3025 20 2833 28 22The mean square between treatments (MSTR) equals Group of answer choices5.861.8723634
Question
To test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly assigned to the 3 treatments. You are given the results below. TreatmentObservationA20302533B22262028C40302822 Note: rearrange this to (columns) in excel: A B C20 22 4030 26 3025 20 2833 28 22The mean square between treatments (MSTR) equals Group of answer choices5.861.8723634
Solution
To calculate the Mean Square Between Treatments (MSTR), we first need to calculate the mean of each treatment group, the grand mean, and the sum of squares between treatments.
Step 1: Calculate the mean of each treatment group For treatment A: (20+30+25+33)/4 = 27 For treatment B: (22+26+20+28)/4 = 24 For treatment C: (40+30+28+22)/4 = 30
Step 2: Calculate the grand mean (27+24+30)/3 = 27
Step 3: Calculate the sum of squares between treatments (SSB) SSB = Σ n*(mean of each group - grand mean)^2 For treatment A: 4*(27-27)^2 = 0 For treatment B: 4*(24-27)^2 = 36 For treatment C: 4*(30-27)^2 = 36 SSB = 0 + 36 + 36 = 72
Step 4: Calculate the Mean Square Between Treatments (MSTR) MSTR = SSB / (number of treatments - 1) MSTR = 72 / (3 - 1) = 36
So, the Mean Square Between Treatments (MSTR) equals 36.
Similar Questions
To test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly assigned to the 3 treatments. You are given the results below. TreatmentObservationA20302533B22262028C40302822 Note: rearrange this to (columns) in excel: A B C20 22 4030 26 3025 20 2833 28 22The null hypothesis is to be tested at the 1% level of significance. The critical value from the table is Group of answer choices16.694.268.0299.39
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